lew@ihuxr.UUCP (09/16/83)
I can except the explanation of the surprize quiz/unexpected hanging "pseudo-paradox" that Jerry Leichter gave. I assume this is the canonical explanation. I would only note that it hinges on the meaning of "know", as Jerry indeed explicitly stated. When I reformulated the problem I was attempting to avoid the involvement of the prisoner/students mental state by substituting "infer" for "know". Note that when Monty Ellis challenged anyone to come up with a way to DETERMINE that the quiz would be on (say) the 15th, he changed the language that he had just reworded himself. That the INFERENCE can be formed is the basis of the original paradox. If you finally nail the formulation down so that it is undeniably self- contradictory, all you are left with is that every finite sequence must have a last element. The paradoxical statement is, "The quiz cannot possibly occur on the last day that it can possibly occur." I hope no one will argue that this is not a self-contradiction. A more prosaic, but really quite clever resolution of the paradox (in its quiz form) was suggested by C. J. Holzwarth. The teacher can give a "pseudo-quiz" every day, with one of them being the real quiz. This obviously wouldn't work for the hanging! This is just like a fable where an elf promises not to remove a marker from a tree where a treasure is hidden, but he places identical markers on every tree in the forest. Lew Mammel, Jr. ihuxr!lew
leichter@yale-com.UUCP (Jerry Leichter) (09/16/83)
Using "infer" in place of "know" has no real effect on Quine's "disolution" of the paradox; you simply have to examine what "infer" ought to mean. If "infer" is to be understood to mean "can derive by a correct proof technique" then the "you can't pick your postulates" argument is quite valid, and you don't have a correct inference, and you can be hung any morning. If "infer" means "can give a plausible sounding argument for", well, plausibility then becomes the whole issue and obviously the teacher/judge will chose not to find your argument "plausible", and you still get nowhere. (If he chooses to call your argument plausible, and accepts this interpretation of the word "infer", then he is simply admitting that he lied to begin with.) -- Jerry decvax!yale-comix!leichter leichter@yale
jim@ism780.UUCP (Jim Balter) (09/17/83)
If the professor says she will give a quiz and it definitely will not occur on the last day that it can possibly occur, and she gives it mid-term, so what? That obviously wasn't the last day it could possibly occur. You have yet to show a valid induction indicating any real paradox. Re the pseudo-quiz "resolution": you may have a problem, but the professor does not, so there is no need for such resolutions. Besides, is a pseudo-quiz really a quiz for some propositions but not one for others? I think Quine has got you (and no doubt most of the rest of us) beat. Jim Balter (decvax!yale-co!ima!jim), Interactive Systems Corp --------